I’m wondering about the same thing. So far, I had no luck finding any workable solution.
While I’m reasonably familiar with WordPress, BuddyPress is still a mystery to me, namely, I have no clue (yet) on how to post an “activity” from within a BuddyPress plugin. The trick here, as I see it, is somehow exposing an API that allows remote sites to insert an “activity” when a button is pressed. Now this is something I know how to do using WP’s standard XML-RPC API for posts/pages/comments and so forth. BuddyPress, however, seems to have a completely different taxonomy, and none of those calls are exposed by WP’s API. Someone has a semi-abandoned project to create a XML-RPC API for BuddyPress, but it was all of a sudden abandoned a few weeks ago, the author claiming to have been victim of hackers, and deleting all documentation, examples, and warning plugin users that he wouldn’t support BP any longer.